Theorems · Theorem · group theory
addOrderOf_eq_card_of_forall_mem_zmultiples
∀ {α : Type u_1} [inst : AddGroup α] {g : α}, (∀ (x : α), x ∈ AddSubgroup.zmultiples g) → addOrderOf g = Nat.card α- Cited by
- 8 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Nat.cardstatement and proof · cited by 844
- AddSubgroup.zmultiplesstatement and proof · cited by 493
- addOrderOfstatement · cited by 208
- Nat.card_zmultiplesproof · cited by 11
- AddSubgroup.eq_top_iff'proof · cited by 11
- AddSubgroup.card_topproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- IsSimpleAddGroup.prime_cardproof · cited by 2
- Infinite.addOrderOf_eq_zero_of_forall_mem_zmultiplesproof · cited by 1
- addOrderOf_eq_card_of_zmultiples_eq_topproof · cited by 1
- IsAddCyclic.card_nsmul_eq_zero_leproof · cited by 1
- IsAddCyclic.extproof · cited by 0
- IsAddCyclic.image_range_cardproof · cited by 0
- addOrderOf_eq_card_of_forall_mem_multiplesproof · cited by 0
- IsAddCyclic.unique_zsmul_zmodproof · cited by 0